I have two different questions I am trying to figure out (quiz tomorrow).
1. Show that if the length of a simple pendulum increases by some small amount delta L, then the period of the pendulum increases by some small amount delta T, where
delta T = delta L
T ............ 2 L
I cant quite figure out how to prove this. I came up with a proportion but I cant quite get it to come out to the answer.
If you use the equations:
T=2*pi*sqrt(L/G) and delta T=2*pi*sqrt(delta L/G) and you divide the first one by the second one, you end up with delta T/T=sqrt(delta L/L) which is not quite the answer.
2. Suppose that some unknown mass is attached to a relaxed vertical spring of unknown k. If it is suddenly released, it falls a distance of 20 cm before being pulled back up by the spring. Determine a numerical value for the period of the oscillation and write the explicit equation that describes the oscillation of the mass.
I know that the Amplitude =.1 m. Im not quite sure how to solve this but one thing I tried is the following:
Fspring=Fg or kx=ma and k=mg/A so thus mgx/A=ma. At the furthest point, where the amplitude is a max (.1m), A=x and thus those cancel, so you are left with g=a. So the max acceleration if 9.8 m/s^2. If you use the standard equation for acceleration which is a=-A*w^2*cos (wt) and pretend the cos value is 1, then the max acceleration equation is a=A*w^2 so if you solve that for w, you get 9.89 rad/s. T=2*pi/w or T=.635 seconds. And the equation is x=.1*cos (9.89t). Does that look right?
Thanks.
1. Show that if the length of a simple pendulum increases by some small amount delta L, then the period of the pendulum increases by some small amount delta T, where
delta T = delta L
T ............ 2 L
I cant quite figure out how to prove this. I came up with a proportion but I cant quite get it to come out to the answer.
If you use the equations:
T=2*pi*sqrt(L/G) and delta T=2*pi*sqrt(delta L/G) and you divide the first one by the second one, you end up with delta T/T=sqrt(delta L/L) which is not quite the answer.
2. Suppose that some unknown mass is attached to a relaxed vertical spring of unknown k. If it is suddenly released, it falls a distance of 20 cm before being pulled back up by the spring. Determine a numerical value for the period of the oscillation and write the explicit equation that describes the oscillation of the mass.
I know that the Amplitude =.1 m. Im not quite sure how to solve this but one thing I tried is the following:
Fspring=Fg or kx=ma and k=mg/A so thus mgx/A=ma. At the furthest point, where the amplitude is a max (.1m), A=x and thus those cancel, so you are left with g=a. So the max acceleration if 9.8 m/s^2. If you use the standard equation for acceleration which is a=-A*w^2*cos (wt) and pretend the cos value is 1, then the max acceleration equation is a=A*w^2 so if you solve that for w, you get 9.89 rad/s. T=2*pi/w or T=.635 seconds. And the equation is x=.1*cos (9.89t). Does that look right?
Thanks.
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